Problem: The grades on a chemistry midterm at Loyola are normally distributed with $\mu = 73$ and $\sigma = 5.5$. Luis earned a $79$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{79 - {73}}{{5.5}}} $ ${ z \approx 1.09}$ The z-score is $1.09$. In other words, Luis's score was $1.09$ standard deviations above the mean.